LECTURE 8 - Bond Development Length and Splices

Bond Development Length and Splices Lecture #8 References:

UP – Institute of Civil Engineering

Summary

Keyword 1.

Flexure consideration

2.

Development length

Lecture #8 Objectives Bond Stress Dev’t Length Tension Bundled Compression

Hooks Cut-Off 1. Flexure 2. Dev’t length 3. Shear Effects 4. Construction Req'ts 5. Other Req'ts

3.

2a. Tension

412.3

2b. Development length check

412.12.3

2c. Compression

412.4

2d. Bundled

412.5, 407.7.6

2e. Hooks

412.6, 407.2

Shear effect 3a. Shear effect

412.11.3

3b. Shear capacity check

412.11.5

4.

Construction

5.

Other requirements

Lap Splice Summary

6.

NSCP 2010

5a. Support and inflection point (tension, compression)

412.13.1, 412.13.3

5b. Structural integrity*

407.14

Lap Splice 6a. Tension

412.16

6b. Compression

412.17 3

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Bond Stress Lecture #8 Objectives Bond Stress Dev’t Length Tension Bundled Compression




 

One assumption in flexural design: No slippage of the bars in relation to the surrounding concrete If bond doesn't exist, unreinforced concrete If bond do exist, bond stresses should also exist to maintain equilibrium

Lap Splice Summary

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Bond Stress Lecture #8 Objectives Bond Stress Dev’t Length Tension Bundled Compression


∑𝐹 = 0;

𝜋𝑑𝑏2 𝑓𝑠2 − 𝑓𝑠1 = 𝜇𝑎𝑣𝑔 𝜋𝑑𝑏 𝑙 4 Let 𝑓𝑠2 − 𝑓𝑠1 = 𝛥𝑓𝑠 gives Δ𝑓𝑠 𝑑𝑏 1 𝜇𝑎𝑣𝑔 = 4𝑙

Lap Splice Summary

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Mechanism of Bond Transfer

Adhesion and Friction


Hooks Cut-Off 1. Flexure 2. Dev’t length 3. Shear Effects 4. Construction Req'ts 5. Other Req'ts Lap Splice Summary

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Mechanism of Bond Transfer Lecture #8 Objectives Bond Stress Dev’t Length Tension Bundled Compression


If splitting occurs, the yield strength of the bars assumed to be part of equilibrium equations will not be developed 8

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Development Length Lecture #8 Objectives



Bond Stress Dev’t Length Tension Bundled Compression




Because the actual bond stresses varies along the length of the bar, the ACI Code uses the concept of development length rather than bond stresses The development length, 𝑙𝑑 , is the shortest length of bar in which the bar stress increase from zero to the yield strength 𝑓𝑦

Lap Splice Summary

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Development Length Lecture #8 Objectives Bond Stress Dev’t Length Tension Bundled Compression


𝑙𝑑

not be less than 𝑙𝑑

Region of maximum bar stress

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Development Length – ACI 12.1

NSCP 412



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Development Length – ACI 12.3

NSCP 412.3.3


𝑓𝑐𝑡

𝑓𝑐𝑡


Properties

Actual

Idealized

Major factors affecting the development length ▪ Bar properties (𝑓𝑦 and 𝑑𝑏 ) ▪ Bar spacing, 𝑐𝑏 (discussion later) ▪ Concrete strength

Lap Splice Summary

ACI 𝒍𝒅 full equation 12

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Development Length – ACI 12.2.4NSCP 412.3.4 Lecture #8 Objectives

1.

Location of Reinforcement (𝜓𝑡 )

2.

Coating of bars(𝜓𝑒 )



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Development Length – ACI 12.2.4NSCP 412.3.4 Lecture #8 Objectives Bond Stress Dev’t Length Tension Bundled Compression

Hooks

3.

Sizes of Reinforcing Bars (𝜓𝑠 )

4.

Lightweight Aggregates (𝜆)

Cut-Off 1. Flexure 2. Dev’t length 3. Shear Effects 4. Construction Req'ts 5. Other Req'ts Lap Splice Summary

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Development Length – ACI 12.2.4NSCP 412.3.4 Lecture #8 Objectives

5.

Confinement term



where 𝑐𝑏 = represents the smaller of the distance from the center of the tension bar or wire to the nearest concrete surface, or one half the center-to-center spacing of reinforcement 𝐾𝑡𝑟 = transverse reinforcement index. Used to account for the contribution of confining reinforcement across possible splitting planes 𝐴𝑡𝑟 = the total cross-sectional area of all transverse reinforcement having the center-to-center spacing, 𝑠, and a yield strength, 𝑓𝑦𝑡 . 𝑛 = number of bars or wires being developed along the plane of splitting

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𝑨𝐯,𝒎𝒊𝒏 =

𝒇′𝒄

𝒃𝒘 𝒔 𝒃𝒘 𝒔 ≥ 𝟏𝟔𝒇𝒚𝒕 𝟑𝒇𝒚𝒕

Development Length – simplified NSCP 412.3.2 Lecture #8 Objectives Bond Stress Dev’t Length Tension Bundled Compression

Substituting lower limit values of 𝑐𝑏 and 𝐾𝑡𝑟 for common design cases:

Hooks Cut-Off 1. Flexure 2. Dev’t length 3. Shear Effects 4. Construction Req'ts 5. Other Req'ts Lap Splice

Case 1

Case 2

Summary

ACI 𝒍𝒅 full equation

ACI 𝒍𝒅 simplified equations

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Development Length – simplified Lecture #8 Objectives Bond Stress Dev’t Length Tension Bundled Compression


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Problem 8.1 Lecture #8 Objectives Bond Stress Dev’t Length Tension Bundled Compression


A 400-mm-wide cantilever beam frames into the edge of a 400-mm-thick wall as shown. To reach Mn, the 3-25mm bars at the top of the beam are stressed to their yield strength at point A at the face of the wall. Compute the minimum embedment of the bars into the wall and the development length in the beam. The concrete is sand/low density concrete with a strength of 25 MPa. The yield strength of the flexural reinforcement is 420 MPa. Construction joints are located at the top and bottom of the beam. The beam has closed 10mm stirrups with fyt = 420 MPa at a spacing of 180 mm throughout its length (the stirrups are not shown). The cover is 40-mm to the stirrups. The three No. 25 bars are inside the 13mm vertical steel in each face of the wall.

Cantilever beam

Summary

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Problem 8.2 – Group Seatwork Lecture #8 Objectives Bond Stress Dev’t Length Tension Bundled Compression

The required reinforcing steel area for the lightweight concrete (fc’ = 21MPa) beam in the figure is given below. The 25-mm top bars (fy = 420MPa) shown are uncoated. Use fyt = 270 MPa. Compute the development lengths using a.) simplified equation (assume stirrup is code compliant) b.) the full equation of ACI equation 12-1 with calculated value of Ktr c.) ACI equation 12-1 with Ktr = 0

40


420 4-25 mm

10 mm stirrups spaced at 200 mm

40 40 mm

750 mm 710 mm

Summary

500 mm 19

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Development Length – Bundled bars Lecture #8 Objectives Bond Stress Dev’t Length Tension Bundled Compression



Greater development lengths are needed when bundled bars are used since part of the surface area of one bar will not be in contact with the concrete


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Compute the development length required for the uncoated bundled bars shown in the figure. Assume fy = 414 MPa, fc’ = 21 MPa and fyt = 270 MPa.


50

50

10mm stirrup at 200mm 500 mm

Lap Splice Summary

250

3 – 25 mm bars 50 mm 21

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Development Length –

Tension ACI 12.11


Moment Capacity 𝜙𝑀𝑛

ACI 𝒍𝒅 full equation Hooks Cut-Off 1. Flexure 2. Dev’t length 3. Shear Effects 4. Construction Req'ts 5. Other Req'ts

Required Moment 𝑀𝑢 O

𝒍𝒅

𝝓𝑴𝒏 < 𝑴𝒖

Lap Splice Summary

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Tension ACI 12.11


Moment Capacity 𝜙𝑀𝑛

ACI 𝒍𝒅 full equation Hooks Cut-Off 1. Flexure 2. Dev’t length 3. Shear Effects 4. Construction Req'ts 5. Other Req'ts Lap Splice Summary

Required Moment 𝑀𝑢 O

𝒍𝒅

𝝓𝑴𝒏 < 𝑴𝒖

To maintain 𝜙𝑀𝑛 > 𝑀𝑢 the slope of the momentcapacity diagram (line OB) cannot be less than the slope of the moment-load diagram (line OA)

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NSCP 412.12.3

Tension ACI 12.11



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NSCP 412.12.3

Tension ACI 12.11



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NSCP 412.4


Compression ACI 12.3



𝑙𝑑𝑐 =

0.24𝑓𝑦 𝜆

𝑓𝑐′

≥ 0.043𝑓𝑦 𝑑𝑏

Note: 𝑙𝑑𝑐 is considerably shorter than 𝑙𝑑

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Development Length – Lecture #8 Objectives



NSCP 412.4


Modification factors for Compression bars



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The forces in the column bars in the figure are to be transferred into the 500-mm thick footing with 32 mm dowels. Determine the development lengths needed for the dowels (a) down into the footing and (b) up into the column fy = 414 MPa and fc’ = 21 MPa (for footing) fc’ = 35 MPa (for column)


ld into column ld into footing

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Hooks Lecture #8 Objectives Bond Stress Dev’t Length Tension Bundled Compression


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Hooks – Mechanism(FBD) Lecture #8 Objectives Bond Stress Dev’t Length Tension Bundled Compression


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Hooks – Mechanism(Stresses) Lecture #8 Objectives Bond Stress Dev’t Length Tension Bundled Compression



Decrease in axial stress is due to bond and friction



Slip measured is relative to the axial stress (180° has a maximum slip 1.75 times the 90°)


Stress diagram and slip measured at points along a hook at a bar stress of 1.25𝑓𝑦 in tests of 90 and 180 degree hooks in No.7 bars

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NSCP 412.6

ACI Requirement Lecture #8 Objectives



For standard hooks, the development length is



𝑙𝑑ℎ = 0.24

𝜓𝑒 𝜆𝑓𝑦 𝑓𝑐′

𝑑𝑏 ≥ 8𝑑𝑏 𝑜𝑟 150𝑚𝑚

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NSCP 412.6

ACI Requirement - ACI 12.5.3 & …4 Lecture #8 Objectives Bond Stress Dev’t Length Tension Bundled Compression


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ACI Requirement - ACI 12.5.3a & …3b Lecture #8 Objectives Bond Stress Dev’t Length Tension Bundled Compression


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Detailing dimension, 𝑙𝑑ℎ 𝜓𝑒 𝜆𝑓𝑦 𝑙𝑑ℎ = 0.24 𝑑𝑏 ′ 𝑓𝑐 Lecture ≥ 8𝑑#8 𝑏 𝑜𝑟 150𝑚𝑚 Objectives



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ACI Standard Hooks (Typical) Lecture #8 Objectives Bond Stress Dev’t Length Tension Bundled Compression


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Problem 8.5 The exterior Lecture #8 end 400x600mm continuous beam frames into a 650-mm square column. The column has 4-36M longitudinal bars. The negative moment reinforcement at the exterior end of the beam consists of 4-25M bars. The concrete is 25 MPa normal weight Objectives concrete. The steel strength is 420 MPa. Design the anchorage of the 4-25M bars into the column. Consider ACI 11.10.2 as well Bond Stress Dev’t Length Tension Bundled Compression


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Problem 8.6 Seatwork (Group) Lecture #8 Objectives Bond Stress Dev’t Length Tension Bundled Compression

Hooks



Determine the development or embedment length required for the epoxy-coated bars of the beam shown in the figure. fy = 414 MPa, fc’ = 28 MPa (a) if the bars are straight, assuming Ktr = 0 (b) if a 180-degree hook is used and (c) if a 90-degree hook is used. Assume 10M stirrups, db = 25M, concrete cover of 50mm 50

250

50 65 mm 115 mm

Cut-Off 1. Flexure 2. Dev’t length 3. Shear Effects 4. Construction Req'ts 5. Other Req'ts

325 mm

Lap Splice Summary

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Bar Cut-off Recall: Location of Reinforcement Lecture #8 Objectives Bond Stress Dev’t Length Tension Bundled Compression


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Bar Cut-off Lecture #8 Objectives Bond Stress Dev’t Length Tension Bundled Compression


Four major factors affecting location of bar cut-offs: 1. When they are no longer needed 2. Development lengths 3. Location of moderately high shear force 4. Constructional requirements 5. Other requirements

Lap Splice Summary

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1

Problem 8.7 Illustration Lecture #8 Objectives Bond Stress Dev’t Length Tension Bundled Compression

Given the following parameters, f'c = 28 MPa, fy = 420 MPa with 100 kN/m load on a 6m (b = 400mm, d = 550mm) beam, the resulting design is 5-25M bars (design strength, 𝜙𝑀𝑛 is 465 kN/m).


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1

Bar Cut-off (Illustration) Lecture #8 Objectives Bond Stress Dev’t Length Tension Bundled Compression


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1

Problem 8.10 Flexure Lecture #8 Objectives Bond Stress Dev’t Length Tension Bundled Compression

Hooks

The beam shown is constructed of normal-weight, 21-MPa concrete and Grade-60 reinforcement. It supports the factored load as shown. Given the cross sections at the points of maximum positive and negative moment, determine the bar cut-off locations of 2-25M bars considering flexural capacities only.


1.2𝑤𝐷 = 6𝑘𝑁/𝑚 & 1.6𝑤𝐿 = 49𝑘𝑁/𝑚

Lap Splice Summary

𝟐 − 𝟑𝟎𝑴 section 𝜙𝑀𝑛 = 253 𝑘𝑁𝑚 𝟐 − 𝟐𝟓𝑴 and 𝟐 − 𝟑𝟎𝑴 section 𝜙𝑀𝑛 = 308 𝐾𝑁𝑚 47

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2

Problem 8.10 Dev’t Length Lecture #8 Objectives Bond Stress Dev’t Length Tension Bundled Compression


The beam shown is constructed of normal-weight, 21-MPa concrete and Grade-60 reinforcement. It supports the factored load as shown. Given the cross sections at the points of maximum positive and negative moment, determine the bar cut-off locations considering development lengths only. 1.2𝑤𝐷 = 6𝑘𝑁/𝑚 & 1.6𝑤𝐿 = 49𝑘𝑁/𝑚

Lap Splice Summary

48

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3

Bar Cut-off Shear Effects Lecture #8 of Shear Objectives Bond Stress Dev’t Length Tension Bundled Compression

Hooks Cut-Off 1. Flexure 2. Dev’t length 3. Shear Effects 4.The Construction Req'tsbe bars should 5. Other Req'ts

anchored into the support Lap Splicefor at least 0.5𝑉𝑢, and Summary preferably 0.75𝑉𝑢. a.

Inclined cracking (shear force) increases the tension force in the flexural reinforcement 49

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Bar Cut-off Shear b. Lecture Stress #8

concentration ▪ Due to reduction of bars (𝐴𝑠 ↓), Bond Stress stresses in bars increases which can Dev’t Length Tension lead to major inclined cracks at the Bundled bar cut-off. (see Figure e) Compression 𝑀𝑢′ 𝑓𝑠 = Hooks 𝜙𝐴𝑠 𝑗𝑑 Objectives

Cut-Off 12.10.3 1. Flexure – Reinforcement shall extend 2. Dev’t length beyond the point at which it is no longer 3. Shear Effects required toReq'ts resist flexure for a distance 4. Construction 5. Other to Req'ts equal d or 12db whichever is greater,

except Lap Spliceat supports of simple spans and at free end of cantilevers Summary

In addition to shear effect, ACI 12.10.3 also accounts for the maximum moment shifts due to changes in loading and support settlement 50

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3

Bar Cut-off Shear c. Lecture Shear #8

strength reduction and loss of ductility ▪ Due to reduced reinforcement, flexure cracks tend to open early whenever any Bond Stress rebar is terminated in a tension zone. Objectives

Dev’t Length Tension Bundled Compression


As a result of the difficulties in satisfying these sections, designers frequently will extend all bars into the supports in simple beams or past points of inflection in continuous beams.

Summary

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3

Problem 8.10 Shear Lecture #8 Objectives Bond Stress Dev’t Length Tension Bundled Compression

Hooks

The beam shown is constructed of normal-weight, 21-MPa concrete and Grade-60 reinforcement. It supports the factored load as shown. Given the cross sections at the points of maximum positive and negative moment, determine the bar cut-off locations considering shear effects only.


1.2𝑤𝐷 = 6𝑘𝑁/𝑚 & 1.6𝑤𝐿 = 49𝑘𝑁/𝑚

Lap Splice Summary


IHST


5

Bar Cut-off Code Requirements Lecture #8 Objectives Bond Stress Dev’t Length Tension Bundled Compression


Extension of tension bars Positive moment: at least 1/3 (simple) or 1/4 (continuous) the reinforcement shall be extended at least 150mm. Negative moment: (beyond pt. of inflection) at least 1/3 shall be extended either 𝑑, 12𝑑𝑏 or 𝑙𝑛 /16 (whichever is greater) 53

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5

Bar Cut-off Code Requirements Lecture #8 Objectives Bond Stress Dev’t Length Tension Bundled Compression


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Summary (ACI) 1. When they are no longer needed Lecture #8 Locate flexural cut-off points Objectives 2. Development lengths Bond Stress Apply development lengths past Dev’t Length Tension the points of maximum stress Bundled a. Compression

b.

Hooks

3.

Cut-Off a. 12.10.3 1. Flexure b. 12.10.5 2. Dev’t length 3. Shear Effects zone 4. Construction Req'ts 5.4. Other Req'ts

b.

6.


2.

Development length

12.11.1 or 12.12.3 Extension into the supports 7.13.2.2 Structural integrity

Lap splice

3.

Shear effect Termination at tension

Constructional requirements 5. Other requirements Lap Splice a.

1.

12.2 to 12.5 𝑙𝑑 formula 12.11.3 Tension bars: 𝑀𝑛 /𝑉𝑢

Shear effects

Summary

Keyword

2a.

Tension

12.2

2b.

Development length check

12.11.3

2c.

Compression

12.3

2d.

Bundled

12.4

2e.

Hooks

12.5

Shear effect 3a.

Shear effect

12.10.3

3b.

Shear capacity check

12.10.5

4.

Construction

5.

Other requirements

6.

ACI 318M (2011)

5a.

Support and inflection point (tension, compression)

12.11.1, 12.12.3

5b.

Structural integrity*

7.13.2.2

Lap Splice 6a.

Tension

12.15

6b.

Compression

12.16

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Summary (NSCP) 1. When they are no longer needed Lecture #8 Locate flexural cut-off points Objectives 2. Development lengths Bond Stress Apply development lengths past Dev’t Length Tension the points of maximum stress Bundled a. Compression

b.

Hooks

3.

Cut-Off a. 412.11.3 1. Flexure b. 412.11.5 2. Dev’t length 3. Shear Effects zone 4. Construction Req'ts 5.4. Other Req'ts

b.

6.


2.

Development length

3.

Shear effect Termination at tension

Constructional requirements 5. Other requirements Lap Splice a.

1.

412.3 to 412.6 𝑙𝑑 formula 412.12.3 Tension bars: 𝑀𝑛 /𝑉𝑢

Shear effects

Summary

Keyword

412.12.1 or 412.12.3 Extension into the supports 407.14 Structural integrity

Lap splice

2a.

Tension

412.3

2b.

Development length check

412.12.3

2c.

Compression

412.4

2d.

Bundled

412.5, 407.7.6

2e.

Hooks

412.6, 407.2

Shear effect 3a.

Shear effect

412.11.3

3b.

Shear capacity check

412.11.5

4.

Construction

5.

Other requirements

6.

NSCP 2010

5a.

Support and inflection point (tension, compression)

412.12.1, 412.12.3

5b.

Structural integrity*

407.14

Lap Splice 6a.

Tension

412.16

6b.

Compression

412.17

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Splices Lecture #8 Objectives Bond Stress Dev’t Length Tension Bundled Compression




Lapped splices, mechanical splices, welded splices, and end-bearing splices

Considerations  Limited bar lengths available and requirements at construction joints (6 m, 7.5 m, 9 m, 10.5 m, 12 m)  Reinforcement congestion  Laps will not be satisfactory for very long lengths (for 29 mm to 36 mm bars) 57

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Splices Lecture #8 Objectives Bond Stress Dev’t Length Tension Bundled Compression


Dywidag THREADBAR® reinforcing bar 58

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Tension Lap Splice Lecture #8 Objectives Bond Stress Dev’t Length Tension Bundled Compression


59

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Failure of a tension Lap Splice without stirrups enclosing the splice

60

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Compression Splices Lecture #8 Objectives Bond Stress Dev’t Length Tension Bundled Compression

Hooks

Compression bars may be spliced by: ▪ Lapping ▪ End Bearing ▪ Welding or Mechanical Devices

Cut-Off 1. Flexure 2. Dev’t length 3. Shear Effects 4. Construction Req'ts 5. Other Req'ts Lap Splice Summary

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Hooks

ALL

The beam shown is constructed of normal-weight, 21-MPa concrete and Grade-60 reinforcement. It supports the factored load as shown. Given the cross sections at the points of maximum positive and negative moment, determine the bar cut-off locations. Consider bar lengths to be 7.5m only. Use Class A splice.


1.2𝑤𝐷 = 6𝑘𝑁/𝑚 & 1.6𝑤𝐿 = 49𝑘𝑁/𝑚

Lap Splice Summary


IHST


Problem 8.10 Lecture #8 Objectives

Lap splice locations



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UP – Institute of Civil (ACI Engineering Standard Bar Details 7.13)

Standard Bar Details (ACI 7.13) Lecture #8 Objectives Bond Stress Dev’t Length Tension Bundled Compression


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Standard Bar Details (ACI 7.13) Lecture #8 Objectives Bond Stress Dev’t Length Tension Bundled Compression


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LECTURE 8 - Bond Development Length and Splices

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